For each of the following statements, select True if the statement

The proportion of museums in D related to Science, History and Archaeology is greater than the proportion of museums in F devoted to the same
Without calculator - i really cannot tell, the ratios seem almost equal.
The ratio of public museums to private museums is greatest for C
False: B has highest ratio.
There is a positive correlation between the number of public museums and the number of visitors per year.
Flase: compare A and B, there is one order of magintude difference in number of visitors althoug number of puplic museums is only 10% different. Similar story for G and H.

1. The proportion of museums in D related to Science, History and Archaeology is greater than the proportion of museums in F devoted to the same

Without calculator:
D: 780/1173 ~ 750/1150 = 15/23 = 45/69
F: 498/775 ~ 500/775 = 100/155 ~ 100/150 = 2/3 = 26/45

With calculator: (Calculator will be available during exam)
D: 780/1173 = 0.66
F: 498/775 = 0.64

So the statement is true.


2. The ratio of public museums to private museums is greatest for C

From a quick glance, it is visible that highest ratio is with the country B.

So the statement is false.


3. There is a positive correlation between the number of public museums and the number of visitors per year.

To answer this question, we need to sort the data on the column public (GMAT IR section provides teh sorting feature)
After the sorting, the data can be found as follows

Number of public museums -**- Visitors per year
163 -********************************- 2058817
203 -*******************************- 11579900 -**- increase in number of visitors
220 -********************************- 2427703 -**- decrease in number of visitors
615 -*******************************- 10123438 -**- increase in number of visitors
713 -*******************************- 19648000 -**- increase in number of visitors
960 -*******************************- 12627700 -**- decrease in number of visitors
973 -*******************************- 56065370 -**- increase in number of visitors
1053 -******************************- 40469600 -**- decrease in number of visitors

Thus, it is evident that number of public museums does not have positive correlation with number of visitors per year.

So the statement is false.

Excel format of the table attached.

St1: The proportion of museums in D related to Science, History and Archaeology is greater than the proportion of museums in F devoted to the same
% for D = 0.66
% for F = 0.64
TRUE

St2:The ratio of public museums to private museums is greatest for C
Ratio for C = 2.67
Ratio for E is greater than 9
hence C is not the greatest.
FALSE

St3: There is a positive correlation between the number of public museums and the number of visitors per year.
Out of 8 countries, 5 show an increase in visitors with increase in # public museums.
I would take that as a sign of POSITIVE correlation since majority is showing a +ve corr. It is not necessary that each country must show this +ve relationship (at least that's my understanding that if we plot this line on a graph with # public museums on X asis and Visitors per year on Y axis, if the slope is up, that's +ve correlation. A positive correlation can co-exist with some elements in the set that might be negatively correlated).
TRUE

Any expert comments would be much apprciated for the 3rd part.

experts!...pls throw some light on..."positive co relation"


Thnks
A

I'm no expert, but I do pretty well on IR. My understanding of positive correlation is: can you infer from the data that a relatively large value on one axis is likely to correspond to a relatively large value on the other axis?

So in the scope of this question, if I ask you to estimate the visitors per year for:

(1) 300-museum country, and

(2) 800-museum country,

Are you going to guess a larger value for the second option?

Then there's probably a positive correlation. (Of course, this is assuming a strictly increasing/decreasing line/curve of best fit; this is going to get more complicated if the data follows a parabolic trend or something.)

Hope that helps a bit.

Country	Total	Related to architecture, art, history	Public ownership	Private ownership	Visitors per year	Staff
Austria	399	79	203	196	11579900	7820
Croatia	221	65	220	1	2427703	1602
Estonia	224	67	163	61	2058817	2203
France	1173	780	1053	120	40469600	24500
Hungary	671	185	615	66	10123438	5807
Netherlands	775	498	713	62	19648000	27810
Spain	1455	679	973	482	56065370	15811
Switzerland	1061	291	960	101	12627700	5939

(Sort ↕ the table by clicking on the headers)

For each of the following statements, select True if the statement can be verified as true based on the information in the table. Otherwise, select False.

A)Yes France has 780 museums while Netherlands has 498
B)Ratio of public to private for the countries are:
1)Austria:203/196=1.03
2)Croatia:220/1=220
3)Estonia:163/61=2.67
4)France:1053/120=8.775
5) Hungary:615/66=9.31
6) Netherlands:713/62=11.5
7)Spain:973/482=2.01
8) Switzerland:960/101=9.5

So answer is false since Croatia has the highest ratio

C)True,per the table when number of public museum decrease/increase the number of visitors per year also decrease/increase in the same pattern

Posted from my mobile device

The answers are False , False and True

The key to solving Quant/IR questions is not having to solve them fully.

Part 1: Proportion of museums in France to Proportion of museums in Netherlands : 780/1173 vs 498/775
Rounding Off : 800/1200 vs 500/800. Second is higher. Hence False

Part 2: Ratio of Public Museums to Private
Estonia: 163/60 ~ 2.8something
Just below this option is France: 1052/120 ~9. We don't need to check others. The answer is False

Part 3: True. We can see that as the #museums increase, the #visitors increase. So +ve correlation is there.

1. The proportion of museums in France related to architecture, art, or history is greater than the proportion of museums in the Netherlands devoted to art, architecture, or history.

The proportion of museums in France related to architecture, art, or history : 780/1173 = 66.49%.
The proportion of museums in the Netherlands devoted to art, architecture, or history: 498/775 = 64.25%

So yes, the statement is true and can be verified from the data given in the table.
Answer - True.

2. The ratio of public museums to private museums is greatest for Estonia.
Looking at the data of the public to Private Museums of the countries, we can see that Croatia has a ratio of 220/1 and rest are obviously less, as is visible in the data.
So no, the statement is not true.
Answer False.


3.There is a positive correlation between the number of public museums and the number of visitors per year.
We can see that as the no. of public museums increase, the no. of visitors also increase for the countries and as the no. of the no. of museums decrease, like for Estonia, the no. of visitors also reduced in comparison to those Croatia.
So increase/decrease in the no. of public museums is directly related to the increase/decrease in the number of visitors per year.

So true, it can be verified from the table.
Answer True.

Maybe I'm nitpicking but 'related to' and devoted to aren't the same thing.

Related to implies they contain Art, x,y,z etc...i.e. they have stuff related to Art, x,y,z amongst other stuff.

Devoted to means dedicated to i.e. contains only Art,x,y,z.

A is a poorly written question.

Hi KarishmaB Bunuel! Regarding C, why is there a positive correlation? The number are varying up and down....Tks! ­

I fail to understand the logic in question C. How is it positively correlated? As mentioned in the case of Austria and Croatia.


Kindly elaborate.

 
Positively correlated does not mean that all the data points have to be in a particular order. It means that the general trend is positive or that majoity of the data points move in a certail direction. There could be few abberations.

As per GMAT, the definitions are as below

1. Charts often show trends over time. They may show that a variable’s values increase, decrease, fluctuate, or change in cycles. They may also show values of different plotted variables changing the same ways or opposite ways.Other things equal, an observed trend over a period is evidence that the same trend extends at least slightly before and after that period. This evidence is stronger the longer the observed trend has lasted and the more varied the conditions it’s lasted through. Generalizing from a longer observed period with more varied conditions is like generalizing from a larger sample.  But the odds increase of other factors disrupting the observed trend at times more distant from the observed period, and in situations whose conditions differ more from those observed.
   
    
2. Two quantitative or ordinal variables are positively correlated if they both tend to be higher in the same cases. They’re negatively correlated if one tends to be higher in cases where the other is lower.

KarishmaB is there any way to estimate proportion of museums in FR and NL?

For these simple one step divisions, you should use the calculator. Practice using it so that you don't forget it exists in the actual test. We can estimate but frankly, after estimating, I will still use the calculator and here is why:

FR = 780/1173
Approximate this to 800/1200. It is a very decent approximation because we have increased the numerator by 20 and denominator by 27. The denominator is greater than the numerator so percentage wise, we have increased both equally. So the actual value here would be very close to 66.6%

NL = 498/775
Approximate this to 500/800. I have over-estimated the denominator which means that the actual percentage will be greater than what I get.
5/8 = 62.5% (Fraction percent equivalents). The actual value will be a bit greater than this so I would guess that FR is higher but it would be better to check since 66.6 isn't much greater than 62.5.

Had the value for FR been 60, I would have been comfortable saying that NL is greater because actual NL value must be greater than 62.5.

Here is a video on fraction percent equivalents: https://youtu.be/HxnsYI1Rws8